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On finite solvable groups decomposable into the product of two nilpotent subgroups

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Abstract

We establish a series of results concerning various properties of a finite solvable groupG=AB with nilpotent subgroupsA andB.

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References

  1. H. Wielandt, “Über Produkte von nilpotenten Gruppen,”Ill. J. Math.,2, No. 4B, 611–618 (1958).

    MATH  MathSciNet  Google Scholar 

  2. O. H. Kegel, “Produkte nilpotenten Gruppen,”Arch. Math.,12, No. 2, 90–93 (1961).

    Article  MATH  MathSciNet  Google Scholar 

  3. O. H. Kegel, “Zur Struktur mehrfach factorisierbarer endlicher Gruppen,”Math. Z.,87, No. 1, 42–48 (1965).

    Article  MATH  MathSciNet  Google Scholar 

  4. F. Gross, “Finite groups which are the product of two nilpotent subgroups,”Bull. Austral. Math. Soc.,9, No. 2, 267–274 (1973).

    Article  MATH  MathSciNet  Google Scholar 

  5. E. Pennington, “On products of finite nilpotent groups,”Math. Z.,134, No. 1, 81–83 (1973).

    Article  MATH  MathSciNet  Google Scholar 

  6. H. Heineken, “Products of finite nilpotent groups,”Math. Ann.,287, No. 4, 643–652 (1990).

    Article  MATH  MathSciNet  Google Scholar 

  7. S. Franciosi, F. de Giovanni, H. Heineken, and M. L. Newell, “On the Fitting length of a soluble product of nilpotent groups,”Arch. Math.,57, No. 4, 313–318 (1991).

    Article  MATH  MathSciNet  Google Scholar 

  8. H. Heineken, “The product of two finite nilpotent groups and its Fitting series,”Arch. Math.,59, No. 3, 209–214 (1992).

    Article  MATH  MathSciNet  Google Scholar 

  9. B. Amberg, S. Franciosi, and F. de Giovanni,Products of Groups, Clarendon Press, Oxford (1992).

    MATH  Google Scholar 

  10. N. S. Chernikov,Groups Decomposable into the Product of Permutable Subgroups [in Russian], Naukova Dumka, Kiev (1987).

    Google Scholar 

  11. N. S. Chernikov, “Periodic locally solvable groups factorized by two locally nilpotent subgroups,”Voprosy Alg. (Gomel'),11, 90–115 (1997).

    MATH  MathSciNet  Google Scholar 

  12. B. Huppert,Endliche Gruppen. I, Springer, Berlin etc. (1967).

    MATH  Google Scholar 

  13. Ph. Hall and G. Higman, “On thep-length ofp-soluble groups and reduction theorems for Burnside's problem,”Proc. London Math. Soc.,6, No. 21, 1–42 (1956).

    Article  MATH  MathSciNet  Google Scholar 

  14. E. G. Bryukhanova, “2-length and 2-period of a finite solvable group,”Alg. Log.,18, No. 1, 9–31 (1979).

    MATH  MathSciNet  Google Scholar 

  15. E. G. Bryukhanova, “Relationship between the 2-length and derived length of a Sylow 2-subgroup of a finite group,”Mat. Zametki,29, No. 2, 161–170 (1981).

    MathSciNet  Google Scholar 

  16. B. Hartley, “Some theorems of Hall-Higman type for small primes,”Proc. London Math. Soc.,41, No. 2, 340–362 (1980).

    Article  MATH  MathSciNet  Google Scholar 

  17. F. Gross, “The 2-length of a finite solvable group,”Pacif. J. Math.,15, No. 4, 1221–1237 (1965).

    MATH  Google Scholar 

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Authors
  1. N. S. Chernikov
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Additional information

Institute of Mathematics, Ukrainian Academy of Sciences, Kiev. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 52, No. 6, pp. 809–819, June, 2000.

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Chernikov, N.S. On finite solvable groups decomposable into the product of two nilpotent subgroups. Ukr Math J 52, 926–939 (2000). https://doi.org/10.1007/BF02591786

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  • DOI: https://doi.org/10.1007/BF02591786

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